Cleaning the soap scum (sorry, long post)

[See bottom of post if you want the Cliff Notes version]

I'm having a heck of a time getting rid of the white hazy look on our shower tile (lesson learned...to regularly clean/treat tiles). One problem is trying to find one good product that will treat soap scum and mildew that is also safe to use on natural stone.

Here is a pic of the shower during the build. The walls are porcelain so most products seem to be safe to use on that. The floor and border on the wall, I guess, falls under the natural stone category. Of course, the grout is colored as well, and I've heard NOT to use anything with bleach in it.
[img]http://onclickpix.com/23042.jpg[/img] (cut/paste link in browser or look in reply below)

In the first pic, there was a couple small spots of mildew in the right hand corner. This is also the area that seems to have a larger problem with the white, hazy, soap scum appearance. It's also the area just below the soap tray seen in the other pic. The hazy look mainly builds up around the perimeter of the floor. Areas that get more foot traffic (middle of the floor) get less hazy...makes sense.

In my search for a cleaner, I went to the place I bought the tile. The lady made a call to someone that suggested using X-14 for the mildew. I picked some up along with another X-14 product (not one of his suggestions) for soap scum (oxy clean w/ citrus something or other). The mildew went away, and I worked on the soap scum not 100% sure what I was using would be the best or safest (desperate person here). The walls cleaned up pretty good, but then the floor still had a white, hazy look. I need to get the floor/grout resealed, but the hazy look made me put it off till I could get some answers/suggestions. The sealer I have, I believe, is made by Black Diamond. The directions say to remove all wax build up, etc before sealing. While the floor doesn't necessarily feel "waxy," it I didn't want to seal over the haze. I also have another product by Black Diamond that is more of a daily use, spray and go product to put on the tile after a shower (similar to Shower Clean).

What do you recommend using to remove soap scum that is safe on natural stone (and limestone as the window sill and shower curb are limestone), colored grout, and porcelain that works well? What to do about the white haze on the shower floor even after the clean up I've already done? I just hope the white haze I see isn't damage from what I've done.